Equivariant Chern numbers and the number of fixed points for unitary torus manifolds
Equivariant Chern numbers and the number of fixed points for unitary torus manifolds
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DOI：
10.4310/mrl.2011.v18.n6.a19
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发表时间：
2011-03
期刊：
影响因子：
--
通讯作者：
Zhi Lu;Qiangbo Tan
中科院分区：
文献类型：
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作者：
Zhi Lu;Qiangbo Tan
设$M^{2n}$是酉环面$（2n）$-流形，即，具有非空不动点集的$（2n）$维定向稳定复连通闭$T^n$-流形。本文证明了$M$等变有界当且仅当对所有$i，j\in {\Bbb N}$，等变Chern数$ =0$，其中$cl ^{T^n}$表示$M$的第1 $个等变Chern类。因此，我们还证明了如果$M$不等价地有界，那么不动点的数量至少是$\lceil{n\over2}\rceil+1$。
Let $M^{2n}$ be a unitary torus $(2n)$-manifold, i.e., a $(2n)$-dimensional oriented stable complex connected closed $T^n$-manifold having a nonempty fixed set. In this paper we show that $M$ bounds equivariantly if and only if the equivariant Chern numbers $ =0$ for all $i, j\in {\Bbb N}$, where $c_l^{T^n}$ denotes the $l$th equivariant Chern class of $M$. As a consequence, we also show that if $M$ does not bound equivariantly then the number of fixed points is at least $\lceil{n\over2}\rceil+1$.